The Vehicular Ad Hoc Network (VANET) plays a vital role in the development of smart cities, especially in ensuring vehicles' safety on roads. However, VANET wireless-based networks face some challenges such as security, stability, communication, and reliability. To resolve these issues, we propose a fuzzy cluster head selection scheme in Cognitive Radio (CR) VANET, which uses the CR technology for the spectrum sensing algorithm. In this technology, the free spectrums of the primary user are utilized by secondary users without any correlation. Moreover, we have considered some input parameters such as vehicles' average velocity, distance, network connectivity level, lane weight and trustworthiness for the fuzzy system based CR VANET in this research. The selected cluster head provides stability and reliability to the cluster compared to the state of art techniques. Extensive experiments were conducted in order to evaluate the effectiveness of the proposed approach. However, simulation results authenticate more stable and secure cluster formation using the proposed fuzzy logic based CR VANET.